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# 6 2solving Inequalities

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### 6 2solving Inequalities

1. 1. Solving Multi-step Inequalities Ch 6 lesson 2
2. 2. Review <ul><li>Solve for m </li></ul>
3. 4. What’s the Deal? <ul><li>In today’s lesson we will solve multi-step inequalities and graph them using a number line. </li></ul><ul><li>These will be similar to the multi-step equations that we worked through n Unit Three. </li></ul>
4. 5. Back to Unit Three, But with an Inequality This should look similar to your first equation. The greater than sign replaces the equal sign.
5. 6. Work the algebra problem just like you would with the = sign <ul><li>Divide negative 1 from both sides </li></ul><ul><li>The answer shows that any number greater than 9 will make a true statement. </li></ul>
6. 7. Fun with graphing <ul><li>We can use a number line to show all the numbers that work for m . </li></ul>-6 -4 -2 0 +2 +4 +6
7. 8. Graph x >9 <ul><li>Start with the number line </li></ul><ul><li>Put an open circle on 5.85 </li></ul><ul><li>Fill in everything to greater than 5.85. </li></ul>-6 -4 -2 0 +2 +4 +6
8. 9. OR Graph x >9 <ul><li>Start with the number line </li></ul><ul><li>You only need to mark 9 </li></ul><ul><li>Put an open circle on 9 </li></ul><ul><li>Fill in everything to greater than 9. </li></ul>9
9. 10. Work the multi-step algebra problem just like you would with the = sign, then graph. -10 This isn't right!
10. 11. Another twist to algebra -10 Whenever you multiply or divide BY A NEGATIVE NUMBER you must flip the inequality. Major Point!
11. 12. Let’s check our work -10 Pick an number from the graphed answer set to see if this works. +10
12. 13. Try one. Solve for x and graph the inequality. <ul><li>c + 7 < -11 </li></ul>
13. 14. Solution <ul><li>c + 7 – 7 < -11 – 7 c + 0 < -18 </li></ul><ul><li>-18 </li></ul>
14. 15. Greater than or equal to has a closed circle. <ul><li>Graph </li></ul>-3
15. 16. Check your work. <ul><li>Could 10 be a solution for x? </li></ul>-3 Ten is part of the graphed solution +10
16. 17. Summary <ul><li>Solving inequalities is similar to solving other algebraic equations. </li></ul><ul><li>Use open circles for greater than (>) or less than (<). </li></ul><ul><li>Use closed circles to show less-than-or equal-to and greater-than-or-equal-to . </li></ul>
17. 18. Assignment: pg. 280 :15 – 29; 36-37; 43, 45